Report of the fit

Fit summary

Description: PV19 version x, parameters for NNLL. Trying the parameters that gave chi2 = 1.65708 for replica 0 when minimised with ceres. Minuit with the same parameters, starting from the same fitcofig, didn’t converge.
Minimiser: ceres
Random seed: 1234
Maximum values allowed for q_T / Q: 0.2
Cut on the error function: 4
Parameterisation: PV19x
Initial parameters fluctuations: True
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \Biggl( \frac{1-\lambda}{1 + g_1(x) b_T^2/4} + \lambda \exp \left(-g_{1B}(x) b_T^2 / 4 \right)\Biggr) \exp\left[- g_2 \log\left(\frac{\zeta}{Q_0^2}\right) b_T^2/4 - g_{2B} \log\left(\frac{\zeta}{Q_0^2}\right) b_T^4/4 \right]g_1(x) = \frac{N_1}{x\sigma} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha}\right)}{2 \sigma^2} \right]g_{1B}(x) = \frac{N_{1B}}{x\sigma_B} \exp\left[ - \frac{\ln^2\left(\frac{x}{\alpha_B}\right)}{2 \sigma_B^2} \right]Q_0^2 = 1\;{\rm GeV}^2 t_0 prescription: True

g_2 N_1 \alpha \sigma \lambda N_{1B} \alpha_B \sigma_B g_{2B}
0.005144 0.68535248 0.21943481 0.3329461 0.66627605 0.0387879 0.075758463 0.34845635 0.019224141

Theory summary

Collinear PDF set: MMHT2014nlo68cl member 0
Collinear FF set: DSS14_NLO_PiSum member 0
b^* prescription: bstarmin
Perturbative order: NNLL
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 270
\chi_{0}^2 = 1.6571
\chi_{mean}^2 = 1.6392
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 1.7007 \pm 0.0802
\langle E \rangle \pm \sigma_{E} = 2.6694 \pm 0.2184

Parameters

Parameter Central replica Average over replicas Fixed
g_2 -0.09141059 -0.07295757 \pm 0.02515211 False
N_1 5.3603904 12.69051436 \pm 47.81474706 False
\alpha 1.0686624 2.06976511 \pm 5.84855393 False
\sigma 0.93749188 0.8379623 \pm 0.29305058 False
\lambda 0.49349918 0.51210077 \pm 0.09098696 False
N_{1B} 0.040693304 0.04323806 \pm 0.29300377 False
\alpha_B 0.052748277 0.29790959 \pm 1.30094204 False
\sigma_B 0.56928194 1.05628826 \pm 21.49245902 False
g_{2B} 0.034354286 0.03183429 \pm 0.01009458 False
Fitted parameter correlation matrix

Fit properties

Global \chi^2 distribution
Global error function distribution
g_2 distribution
N_1 distribution
\alpha distribution
\sigma distribution
\lambda distribution
N_{1B} distribution
\alpha_B distribution
\sigma_B distribution
g_{2B} distribution

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.4814 0.0307 0.5121
E605_Q_8_9 8 0.9948 0.0176 1.0124
E605_Q_10.5_11.5 10 0.494 0.1396 0.6336
E288_200_Q_4_5 4 0.9291 0.8595 1.7885
E288_200_Q_5_6 5 2.3107 0.3547 2.6654
E288_200_Q_6_7 6 0.7947 0.2112 1.0059
E288_200_Q_7_8 7 0.9887 0.032 1.0206
E288_200_Q_8_9 8 0.7359 0.0059 0.7419
E288_300_Q_4_5 4 0.7784 0.3426 1.121
E288_300_Q_5_6 5 1.3997 0.1 1.4997
E288_300_Q_6_7 6 1.042 0.0398 1.0818
E288_300_Q_7_8 7 0.3439 0.0425 0.3864
E288_300_Q_8_9 8 0.3919 0.0384 0.4303
E288_400_Q_5_6 5 0.9446 0.001 0.9456
E288_400_Q_6_7 6 0.5281 0.0068 0.5349
E288_400_Q_7_8 7 0.2499 0.0139 0.2637
E288_400_Q_8_9 8 0.5613 0.0126 0.574
E288_400_Q_11_12 11 0.5749 0.0068 0.5817
E288_400_Q_12_13 12 0.5394 0.0113 0.5507
E288_400_Q_13_14 12 0.3455 0.0363 0.3817
STAR_510 7 1.192 0.0136 1.2056
CDF_RunI 25 0.6522 0.1484 0.8006
CDF_RunII 26 1.2759 0.0074 1.2833
D0_RunI 12 0.6652 0.0018 0.667
D0_RunII 5 0.9114 0.2907 1.2022
D0_RunIImu 3 0.1197 0.0844 0.2041
LHCb_7TeV 7 1.945 0.8427 2.7877
LHCb_8TeV 7 1.9245 1.453 3.3775
LHCb_13TeV 7 1.4927 0.2893 1.782
CMS_7TeV 4 2.8928 0 2.8928
CMS_8TeV 4 1.4845 0.1782 1.6627
ATLAS_7TeV_y_0_1 6 6.9545 1.0911 8.0455
ATLAS_7TeV_y_1_2 6 4.9261 0.4825 5.4086
ATLAS_7TeV_y_2_2.4 6 1.8076 0.0099 1.8176
ATLAS_8TeV_y_0_0.4 6 4.7783 0.9776 5.756
ATLAS_8TeV_y_0.4_0.8 6 6.6974 1.5469 8.2443
ATLAS_8TeV_y_0.8_1.2 6 4.3581 0.6689 5.027
ATLAS_8TeV_y_1.2_1.6 6 2.9433 0.4249 3.3682
ATLAS_8TeV_y_1.6_2 6 2.5563 0.2696 2.8259
ATLAS_8TeV_y_2_2.4 6 1.2834 0.1619 1.4453
ATLAS_8TeV_Q_46_66 4 0.7685 0.0368 0.8053
ATLAS_8TeV_Q_116_150 8 1.1501 0.0073 1.1574
Total 319 - - 1.6571
Mean-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.632 0.0898 0.7218
E605_Q_8_9 8 1.2311 0.048 1.2791
E605_Q_10.5_11.5 10 0.3645 0.1015 0.466
E288_200_Q_4_5 4 0.4534 0.4421 0.8956
E288_200_Q_5_6 5 1.3314 0.2707 1.6021
E288_200_Q_6_7 6 0.5796 0.1765 0.7562
E288_200_Q_7_8 7 0.9051 0.0334 0.9385
E288_200_Q_8_9 8 0.9342 0.0128 0.9469
E288_300_Q_4_5 4 0.5336 0.16 0.6935
E288_300_Q_5_6 5 1.1461 0.0595 1.2056
E288_300_Q_6_7 6 0.9439 0.0265 0.9704
E288_300_Q_7_8 7 0.326 0.033 0.359
E288_300_Q_8_9 8 0.2817 0.0393 0.321
E288_400_Q_5_6 5 1.0811 0.0171 1.0982
E288_400_Q_6_7 6 0.6129 0.0299 0.6427
E288_400_Q_7_8 7 0.2957 0.0462 0.3419
E288_400_Q_8_9 8 0.7447 0.0408 0.7856
E288_400_Q_11_12 11 0.839 0.0141 0.8531
E288_400_Q_12_13 12 0.8667 0.0173 0.884
E288_400_Q_13_14 12 0.8895 0.066 0.9555
STAR_510 7 1.1469 0.0372 1.1841
CDF_RunI 25 0.5739 0.1421 0.716
CDF_RunII 26 1.2356 0.006 1.2416
D0_RunI 12 0.6384 0.0007 0.6391
D0_RunII 5 1.0845 0.2943 1.3788
D0_RunIImu 3 0.022 0.0333 0.0554
LHCb_7TeV 7 1.682 0.8471 2.5291
LHCb_8TeV 7 1.8199 1.3821 3.202
LHCb_13TeV 7 1.3368 0.2691 1.6059
CMS_7TeV 4 2.8768 0 2.8768
CMS_8TeV 4 1.5098 0.1835 1.6933
ATLAS_7TeV_y_0_1 6 6.9378 1.0929 8.0307
ATLAS_7TeV_y_1_2 6 4.8183 0.4907 5.3091
ATLAS_7TeV_y_2_2.4 6 1.6825 0.01 1.6924
ATLAS_8TeV_y_0_0.4 6 4.7797 1.0131 5.7928
ATLAS_8TeV_y_0.4_0.8 6 6.5292 1.5932 8.1224
ATLAS_8TeV_y_0.8_1.2 6 4.3571 0.6881 5.0452
ATLAS_8TeV_y_1.2_1.6 6 2.9724 0.4409 3.4133
ATLAS_8TeV_y_1.6_2 6 2.4292 0.2746 2.7039
ATLAS_8TeV_y_2_2.4 6 1.1482 0.1534 1.3016
ATLAS_8TeV_Q_46_66 4 0.716 0.0522 0.7682
ATLAS_8TeV_Q_116_150 8 1.1316 0.0063 1.1379
Total 319 - - 1.6392
Average-over-replicas \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 0.4513 \pm 0.2372 0.1896 \pm 0.3088 0.6409 \pm 0.2801
E605_Q_8_9 8 1.0562 \pm 0.2814 0.1272 \pm 0.1971 1.1835 \pm 0.3074
E605_Q_10.5_11.5 10 0.4632 \pm 0.2561 0.1994 \pm 0.2873 0.6626 \pm 0.2126
E288_200_Q_4_5 4 0.5274 \pm 1.2228 1.1102 \pm 1.211 1.6376 \pm 0.4142
E288_200_Q_5_6 5 2.0643 \pm 0.6861 0.4911 \pm 0.6232 2.5554 \pm 0.35
E288_200_Q_6_7 6 0.6389 \pm 0.4078 0.3042 \pm 0.3518 0.9431 \pm 0.2271
E288_200_Q_7_8 7 0.8732 \pm 0.2666 0.1173 \pm 0.1617 0.9905 \pm 0.2335
E288_200_Q_8_9 8 0.6884 \pm 0.1436 0.0814 \pm 0.1216 0.7698 \pm 0.1338
E288_300_Q_4_5 4 0.4581 \pm 0.7823 0.5634 \pm 0.7213 1.0215 \pm 0.2611
E288_300_Q_5_6 5 1.1437 \pm 0.4287 0.2822 \pm 0.3808 1.4259 \pm 0.3134
E288_300_Q_6_7 6 0.8482 \pm 0.365 0.1702 \pm 0.2521 1.0184 \pm 0.3057
E288_300_Q_7_8 7 0.2174 \pm 0.2377 0.1527 \pm 0.2259 0.3701 \pm 0.1712
E288_300_Q_8_9 8 0.3347 \pm 0.1636 0.1135 \pm 0.1742 0.4481 \pm 0.0798
E288_400_Q_5_6 5 0.7207 \pm 0.4038 0.1706 \pm 0.2432 0.8913 \pm 0.3673
E288_400_Q_6_7 6 0.4046 \pm 0.3472 0.1178 \pm 0.1577 0.5224 \pm 0.3521
E288_400_Q_7_8 7 0.1702 \pm 0.2897 0.1243 \pm 0.1923 0.2944 \pm 0.2781
E288_400_Q_8_9 8 0.524 \pm 0.1912 0.0937 \pm 0.1567 0.6176 \pm 0.1931
E288_400_Q_11_12 11 0.5413 \pm 0.1319 0.0481 \pm 0.0671 0.5894 \pm 0.136
E288_400_Q_12_13 12 0.5298 \pm 0.0984 0.0549 \pm 0.0748 0.5847 \pm 0.1012
E288_400_Q_13_14 12 0.3521 \pm 0.1254 0.0806 \pm 0.0861 0.4327 \pm 0.1506
STAR_510 7 1.0753 \pm 0.2297 0.1179 \pm 0.1801 1.1932 \pm 0.1511
CDF_RunI 25 0.6244 \pm 0.1758 0.1993 \pm 0.1712 0.8238 \pm 0.0478
CDF_RunII 26 1.2861 \pm 0.2307 0.0594 \pm 0.0772 1.3455 \pm 0.2215
D0_RunI 12 0.628 \pm 0.1273 0.0682 \pm 0.0998 0.6961 \pm 0.0743
D0_RunII 5 0.6847 \pm 0.6844 0.4929 \pm 0.5676 1.1776 \pm 0.3549
D0_RunIImu 3 -0.3655 \pm 0.6009 0.5434 \pm 0.5577 0.1778 \pm 0.2622
LHCb_7TeV 7 1.7619 \pm 0.7676 1.068 \pm 0.7369 2.8299 \pm 0.194
LHCb_8TeV 7 1.9023 \pm 0.9789 1.5711 \pm 0.9045 3.4734 \pm 0.3695
LHCb_13TeV 7 1.4037 \pm 0.4286 0.3604 \pm 0.4047 1.7641 \pm 0.1
CMS_7TeV 4 2.9071 \pm 0.056 0.0 \pm 0.0 2.9071 \pm 0.056
CMS_8TeV 4 1.4376 \pm 0.2788 0.2545 \pm 0.2312 1.6921 \pm 0.1362
ATLAS_7TeV_y_0_1 6 7.0564 \pm 0.9804 1.1916 \pm 0.5676 8.2479 \pm 0.7257
ATLAS_7TeV_y_1_2 6 5.0049 \pm 0.4967 0.5612 \pm 0.3415 5.5662 \pm 0.3634
ATLAS_7TeV_y_2_2.4 6 1.8566 \pm 0.1681 0.0263 \pm 0.0353 1.8829 \pm 0.1652
ATLAS_8TeV_y_0_0.4 6 5.0304 \pm 0.7671 1.0682 \pm 0.5054 6.0986 \pm 0.6327
ATLAS_8TeV_y_0.4_0.8 6 6.7856 \pm 0.7991 1.6653 \pm 0.7173 8.4509 \pm 0.4889
ATLAS_8TeV_y_0.8_1.2 6 4.321 \pm 0.4412 0.6707 \pm 0.3289 4.9918 \pm 0.3395
ATLAS_8TeV_y_1.2_1.6 6 2.9251 \pm 0.4087 0.4814 \pm 0.3273 3.4065 \pm 0.2666
ATLAS_8TeV_y_1.6_2 6 2.6986 \pm 0.4661 0.3245 \pm 0.3115 3.0231 \pm 0.3412
ATLAS_8TeV_y_2_2.4 6 1.5245 \pm 0.5671 0.2544 \pm 0.227 1.7789 \pm 0.5397
ATLAS_8TeV_Q_46_66 4 0.6217 \pm 0.3154 0.2169 \pm 0.3072 0.8386 \pm 0.1187
ATLAS_8TeV_Q_116_150 8 1.0732 \pm 0.1956 0.1106 \pm 0.1839 1.1838 \pm 0.067
Total 319 - - 1.7007 \pm 0.0802

TMDs in k_T space

TMD PDF of the d at Q = 2 GeV and x = 0.001
TMD PDF of the d at Q = 2 GeV and x = 0.01
TMD PDF of the d at Q = 2 GeV and x = 0.1
TMD PDF of the d at Q = 2 GeV and x = 0.5
TMD PDF of the d at Q = 2 GeV and x = 0.9

Data-theory comparison

E605_Q_7_8 data-theory comparison
E605_Q_8_9 data-theory comparison
E605_Q_10.5_11.5 data-theory comparison
E288_200_Q_4_5 data-theory comparison
E288_200_Q_5_6 data-theory comparison
E288_200_Q_6_7 data-theory comparison
E288_200_Q_7_8 data-theory comparison
E288_200_Q_8_9 data-theory comparison
E288_300_Q_4_5 data-theory comparison
E288_300_Q_5_6 data-theory comparison
E288_300_Q_6_7 data-theory comparison
E288_300_Q_7_8 data-theory comparison
E288_300_Q_8_9 data-theory comparison
E288_400_Q_5_6 data-theory comparison
E288_400_Q_6_7 data-theory comparison
E288_400_Q_7_8 data-theory comparison
E288_400_Q_8_9 data-theory comparison
E288_400_Q_11_12 data-theory comparison
E288_400_Q_12_13 data-theory comparison
E288_400_Q_13_14 data-theory comparison
STAR_510 data-theory comparison
CDF_RunI data-theory comparison
CDF_RunII data-theory comparison
D0_RunI data-theory comparison
D0_RunII data-theory comparison
D0_RunIImu data-theory comparison
LHCb_7TeV data-theory comparison
LHCb_8TeV data-theory comparison
LHCb_13TeV data-theory comparison
CMS_7TeV data-theory comparison
CMS_8TeV data-theory comparison
ATLAS_7TeV_y_0_1 data-theory comparison
ATLAS_7TeV_y_1_2 data-theory comparison
ATLAS_7TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_y_0_0.4 data-theory comparison
ATLAS_8TeV_y_0.4_0.8 data-theory comparison
ATLAS_8TeV_y_0.8_1.2 data-theory comparison
ATLAS_8TeV_y_1.2_1.6 data-theory comparison
ATLAS_8TeV_y_1.6_2 data-theory comparison
ATLAS_8TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_Q_46_66 data-theory comparison
ATLAS_8TeV_Q_116_150 data-theory comparison